If you want to change your iCloud ID to another existing ID (username) you'll have to delete the account, create a new account with the other ID, and migrate your data to the new account.
Before deleting the account, if you have any photos in photo stream that are not in your camera roll or backed up somewhere else save these to your camera roll or you will lose them. To do this, open the photo stream album in the thumbnail view, tap Edit, tap all the photos you want to save, tap Share, then tap Save to Camera Roll.
Once this is done, go to Settings>iCloud, scroll to the bottom and tap Delete Account. When prompted about what to do with the iCloud data, be sure to select Keep On iPhone. Next, set up a new iCloud account using the Apple ID (username) you want to use. (If you haven't yet created this ID you can tap Get free Apple ID at the bottom to do so.) Then turn iCloud data syncing for contacts, etc. back to On, and when prompted about merging with iCloud, choose Merge. This will upload the data to the new account.